The nearest definite pair for the Hermitian generalized eigenvalue problem

DOI10.1016/S0024-3795(99)00026-9zbMath0947.65042WikidataQ56998899 ScholiaQ56998899MaRDI QIDQ1970433

Sheung Hun Cheng, Nicholas J. Higham

Publication date: 21 March 2000

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplesHermitian matricesgeneralized eigenvalue problemfield of valuesnumerical radiusCrawford number

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items

Subspace Acceleration for the Crawford Number and Related Eigenvalue Optimization Problems, Crawford numbers of companion matrices, A note on numerical ranges of tensors, On computing the generalized Crawford number of a matrix, Numerical range for weighted Moore-Penrose inverse of tensor, Eigenvalue characterization of some structured matrix pencils under linear perturbation, Computational geometry of positive definiteness, Partial Smoothness of the Numerical Radius at Matrices Whose Fields of Values are Disks, Nonlinear Eigenvector Methods for Convex Minimization over the Numerical Range, Distance Problems for Hermitian Matrix Pencils with Eigenvalues of Definite Type, Definite triples of Hermitian matrices and matrix polynomials, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems

Uses Software

• PDFIND

Cites Work

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• Computing a nearest symmetric positive semidefinite matrix
• Symmetric matrix pencils
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• Perturbation bounds for the definite generalized eigenvalue problem
• The boundary of the numerical range of matrix polynomials
• Generalized eigenvalues of a definite Hermitian matrix pair
• Perturbation theorems for the generalized eigenvalue problem
• Computing the numerical radius
• Computing the field of values and pseudospectra using the Lanczos method with continuation
• Matrix Analysis
• A Stable Generalized Eigenvalue Problem
• On Perturbations of Matrix Pencils with Real Spectra
• An algorithm for computing the numerical radius
• Algorithm 646